“Lisa the Simpson” puzzle

Fans of Richard Wiseman’s Friday puzzle will have noticed a particularly lovely one last week. Why is this correct?

As Richard explained, you simply have to mirror the left hand digit and move it over to the right hand digit in order to create a shape like a fish, a figure eight or a triangle.

This reminded me of a puzzle from an episode of The Simpsons titled “Lisa the Simpson”. When I met David X. Cohen, part of the writing team for that episode, he told me that he had suggested the puzzle and showed me his original sketches.

5.4 Lisa puzzle script 1

The puzzle, almost as it appeared in the episode, is the third line on this page of doodles. Solving the problem relies on noticing that the left and right halves of each symbol are mirror images of each other. The right half of the first symbol is 1, and the left half is its reflection. The right half of the second symbol is 2, and the left half is its reflection. The pattern continues with 3, 4, and 5, so the sixth symbol would be 6 joined to its own reflection.

The upper line suggests Cohen was thinking of using the sequence (3, 6, 9), but this idea was abandoned, probably because the fourth element, 12, would have required two digits.

The second and fourth lines, which show the sequences (1, 4, 2, 7) and (1, 4, 2), were also abandoned. I cannot identify the patterns behind these two sequences, and Cohen can no longer remember what he had in mind. Maybe you have some ideas.

Ps. If you want to be reminded of Richard Wiseman’s Friday puzzle each week, then follow him on twitter @RichardWiseman. And you can find his daily blog at http://richardwiseman.wordpress.com/blog-2/

PPs. And if you have not caught any of Richard’s brilliant “Bets” youtube videos, then they are really worth watching. The latest video has just been released.